A method for judging the quality of anisotropic meshes

Abstract

The present invention discloses a method for judging the quality of anisotropic meshes, comprising the following steps: for a generated quadrilateral mesh or triangular mesh, finding the ideal lengths of its u and v direction vectors in its background mesh, and forming a complete parallelogram by drawing parallel lines, that is, the ideal quadrilateral mesh corresponding to the actual mesh; converting the quadrilateral mesh or triangular mesh respectively so that the converted graphics can represent the anisotropic characteristics of the original mesh and coincide with the center of the ideal quadrilateral, and calculating the overlapping area of ​​the two graphics; judging the degree of similarity between the actual mesh and the ideal mesh based on the overlapping area, and determining the mesh quality. The present invention can more accurately judge the quality of anisotropic meshes by comparing the actual mesh with the ideal mesh in the background mesh. The mesh quality is converted into the area of ​​the overlapping area of ​​the two graphics, and the calculation result is more intuitive and easy to understand, with fewer calculation steps and faster speed.

Description

Technical Field

[0001] The present invention relates to the technical field of grid generation quality, and in particular to a method for judging anisotropic grid quality. Background Art

[0002] With the rapid development of computer science and technology, numerical simulation technology has been applied in more and more fields. Mesh generation is the first step in numerical simulation, and the quality of the mesh directly affects the accuracy and speed of numerical analysis. Therefore, studying efficient and high-quality mesh generation is a very meaningful topic.

[0003] After decades of continuous efforts and breakthroughs by numerous experts and scholars at home and abroad, structured grid generation methods have become increasingly mature. At present, unstructured grid generation algorithms have begun to develop from isotropic grids to anisotropic grids.

[0004] The existing quality judgment method of isotropic mesh is as follows:

[0005] The evaluation indicators of triangular mesh units mainly include: unit internal angle, unit distortion angle, and the degree of closeness to an equilateral triangle.

[0006] Unit interior angle: the size of the three interior angles of a triangle.

[0007] Unit distortion angle: This index characterizes the degree of distortion of the unit within the unit surface. Figure 1 As shown, it is defined as: the complementary angle of the minimum angle among the angles between the midpoints of the corresponding sides, that is, the twist angle θ of the triangle unit skew =90°-min(α1, α2, α3), α1, α2, α3 are the mean interior angles.

[0008] Closeness to an equilateral triangle: In an isotropic triangular mesh, an equilateral triangle is optimal. Generally, the following formula is used to determine how close a triangle is to an equilateral triangle:

[0009]

[0010] Here, α is the vector of the three sides of the triangle. The final calculated value is between 0 and 1. The closer the value of ɑ is to 1, the closer the shape of the element is to an equilateral triangle, and the higher the element quality. When ɑ = 1, it indicates that the element is an equilateral triangle and has the best element quality.

[0011] The evaluation indicators of quadrilateral grid cells mainly include:

[0012] Unit side length ratio: For quadrilateral elements, the ratio of the longest side length to the shortest side length becomes the side length ratio of the quadrilateral element. In order to ensure the quality of the final mesh, it should be properly controlled. The ideal side length ratio is 1, that is, a square element.

[0013] Unit twist angle: The unit twist angle of a quadrilateral is the smaller angle of the angle between the midpoints of two pairs of sides. The unit twist angle is between 0° and 90°. Figure 2 As shown in the figure, the smaller the unit distortion angle is, the smaller the degree of distortion of the unit is. The calculation formula is as follows:

[0014] θ=90°-min(δ1,δ2)

[0015] Unit warping angle: For a quadrilateral generated on a surface, since three points can determine a face, the fourth point rarely falls on this face, which will produce a dihedral angle in space. The unit warping angle is defined as the larger value of the two dihedral angles. Figure 3 As shown in the figure, the larger the warping angle, the greater the degree of non-coplanarity of the four points. When generating the actual mesh, this also means that the mesh here is too sparse and mesh refinement is needed to improve the warping angle.

[0016] Jacobi ratio: Jacobi ratio describes the measure of how close a unit is to the ideal unit. The value range of Jacobi ratio is from -1 to 1, where 1 represents the best ideal unit, close to 0 means that the angle of a certain angle is close to 180°, and less than 0 means that a concave unit appears. Figure 4 As shown, the Jacobian ratio is calculated as follows:

[0017]

[0018] |J|1=|l1l4sinθ1|=|(x2-x1)(y4-y1)-(x4-x1)(y2-y1)|

[0019] The method for calculating |J|2, |J|3, and |J|4 is the same as |J|1.

[0020] The above are some common mesh quality assessment criteria, but they are all based on isotropic meshes. Since the solutions to some complex engineering problems in practice are anisotropic, anisotropic meshing is an effective pre-processing technique to achieve efficient solutions using fewer mesh elements and better quality for finite element analysis. For anisotropic meshes, the current method is to introduce the Riemannian metric to assess mesh quality.

[0021] Both isotropic and anisotropic meshes are relative to the metric space. For example, in an isotropic mesh defined in a Euclidean metric field, the mesh node sizes are the same along all directions. However, in an anisotropic mesh defined in a Euclidean metric field, the mesh node sizes along the eigenvectors are different. In contrast, in an anisotropic mesh defined in a Riemannian metric tensor field, the mesh node sizes are the same along all directions. Therefore, the Riemannian metric can be used to determine the quality of anisotropy.

[0022] For example, in the paper "Variable Metric Anisotropic Grid Generation Algorithm and Grid Matching for Anisotropic Elliptic Partial Differential Equations", the anisotropic metric is defined as the existence of a Riemannian metric M on a given two-dimensional region, which is a symmetric positive definite matrix and is orthogonally decomposed as follows:

[0023]

[0024] Where: Λ is the size field; λ1 and λ2 are eigenvalues; h1 and h2 are the expected sizes in the vector direction; E is the direction field; e1 and e2 are the unit orthogonalized eigenvectors, and θ is the rotation angle function.

[0025] The ellipse controlled by the Riemann metric matrix is ​​as follows Figure 5 As shown, if the distance between two points p and q on Ω is small enough, then the metric change between the two points is slight, and the approximate distance between the two points in the given metric field can be obtained:

[0026]

[0027] Where: M avg =(M(p)+M(q)) / 2 is the average of the two-point metrics.

[0028] Similarly, the approximate triangle area formula in a given metric field can be given:

[0029]

[0030] Where:

[0031]

[0032] S(Δ abc ) is Δ abc In Euclid's area, the anisotropic mesh quality formula is:

[0033]

[0034] Where: S M (t) is the approximate triangle area; L M (t i ) is the side length of the triangle. When q t= 1, that is, the triangle is an equilateral triangle under the current metric. To compare the quality of the mesh, use the average mesh quality q avg As the basis for judgment, and assuming the total number of grids is N, then:

[0035]

[0036] This method for determining anisotropic mesh quality has the following problems:

[0037] (1) In the calculation formula, the distance between two points p and q is required to be small enough, and the metric change between the two points is subtle, so M is used. avg =(M(p)+M(q)) / 2) to replace the two-point metric average. However, when this method is actually used, the size of the grid may not meet the restriction conditions. For a larger grid, the distance between adjacent nodes will also be larger. If there is a Riemannian metric in the two-dimensional region that changes nonlinearly, then M avg =(M(p)+M(q)) / 2) instead of the formula of the two-point metric average will cause a certain error in the calculation result, which greatly affects the judgment of the grid quality.

[0038] (2) When judging the quality of each grid, a large number of matrix calculations are required. When the total number of grids is N, the quality of the N grids needs to be averaged, which will consume a lot of time and greatly affect the calculation efficiency.

[0039] Since the size values ​​of anisotropic mesh elements are different in different directions, it is necessary to establish a suitable background mesh to define the size value at a certain point in space. The size value of each node in the two directions of the eigenvector u and v is used to guide the generation of the anisotropic mesh. When generating meshes, for models with more complex shapes, it is inevitable that mesh elements of poor quality will be generated. However, the quality of the mesh has a great impact on the accuracy of the solution. Therefore, when the quality of the automatically generated initial mesh is poor, in order to ensure that the simulation analysis process can proceed normally, the quality of the initial mesh must be optimized. At this time, it is necessary to establish a set of mesh quality evaluation standards to provide scientific guidance for the direction of mesh optimization. Summary of the Invention

[0040] The purpose of the present invention is to provide a method for judging the quality of anisotropic grids.

[0041] In order to achieve the above object, the present invention provides the following technical solutions:

[0042] The present invention provides a method for determining the quality of anisotropic meshes, comprising the following steps:

[0043] S1: For a generated quadrilateral mesh or triangular mesh, find the ideal lengths of its u and v direction vectors in the background mesh, and draw parallel lines to form a complete parallelogram, which is the ideal quadrilateral mesh corresponding to the actual mesh.

[0044] S2: Convert the quadrilateral mesh or triangular mesh separately so that the converted graphics can represent the anisotropic characteristics of the original mesh and coincide with the center of the ideal quadrilateral, and calculate the overlapping area of ​​the two graphics;

[0045] S3: Determine the mesh quality by judging the similarity between the actual mesh and the ideal mesh based on the overlapping area.

[0046] Furthermore, for the quadrilateral mesh, the overlapping area calculation process in step S2 is as follows: first, the quadrilateral mesh is proportionally enlarged or reduced so that its area is equal to the area of ​​the ideal quadrilateral mesh, then it is coincident with the center of the ideal quadrilateral, and the actual quadrilateral is projected onto the ideal quadrilateral plane to calculate the overlapping area S 重合 , the closer the overlapping area is to the area of ​​the ideal grid, the higher the grid quality.

[0047] Furthermore, in step S3, for the generated quadrilateral mesh, the mesh quality Q 四边形 =α1*α2, α1=min(S 实 , S 理 ) / max(S 实 , S 理 ), α2=S 重合 / S 理 , where S 实 is the area of ​​the actual quadrilateral mesh, S 理 is the area of ​​the ideal quadrilateral mesh, α1 and α2 are two parameters that are set. α1 represents the degree of closeness between the actual mesh area and the ideal mesh area, and α2 represents the degree of closeness between the anisotropic size of the actual quadrilateral in the u and v directions and the anisotropic size of the ideal quadrilateral mesh in the u and v directions at its location.

[0048] Furthermore, in step S2, for the generated triangular mesh, it is first necessary to convert the triangular mesh into an anisotropic quadrilateral mesh.

[0049] Furthermore, the process of converting the triangular mesh into an anisotropic quadrilateral mesh is as follows: obtain the u and v directions of the ideal triangular mesh, and translate the straight lines in the u and v directions up, down, left, and right respectively, so that the parallelogram composed of the four sides just surrounds the triangle. At this time, the parallelogram represents the anisotropic characteristics of the triangle in the u and v directions.

[0050] Furthermore, for triangular meshes, the overlapping area calculation process in step S2 is as follows: the converted quadrilateral mesh is proportionally enlarged or reduced so that its area is equal to the area of ​​the ideal quadrilateral mesh, and then coincides with the center of the ideal quadrilateral, and the actual quadrilateral is projected onto the ideal quadrilateral plane to calculate the overlapping area S 重合 , the closer the overlapping area is to the area of ​​the ideal grid, the higher the grid quality.

[0051] Furthermore, for the generated triangular mesh, the mesh quality Q 三角形 =β1*β2*β3, β1=2*S 三角形 / S 平行四边形 , β2=min(S 平行四边形 , S 理 ) / max(S 平行四边形 , S 理 ), β3=S 重合 / S 理 , where S 平行四边形 is the area of ​​the converted quadrilateral mesh, S 理 is the area of ​​the ideal quadrilateral mesh, β1, β2, and β3 are three parameters that are set. β1 represents the degree of closeness between the actual triangular mesh and the area of ​​the converted parallelogram, β2 represents the degree of closeness between the area of ​​the converted parallelogram and the ideal mesh, and β3 represents the degree of closeness between the anisotropic size of the converted parallelogram in the u and v directions and the anisotropic size of the ideal quadrilateral mesh at its location in the u and v directions.

[0052] Compared with the existing technology, it has the following beneficial effects:

[0053] This paper provides a method for determining anisotropic mesh quality. By comparing the actual mesh with an ideal mesh in a background mesh, the quality of the anisotropic mesh can be more accurately determined. Mesh quality is converted into the area of ​​the overlap between two graphics. The result is more intuitive and easier to understand, with fewer calculation steps and faster computation time. This method can provide scientific guidance for mesh optimization and generate higher-quality anisotropic meshes. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments described in the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0055] Figure 1 Defined for the element twist angle.

[0056] Figure 2 Schematic diagram of unit twist angle.

[0057] Figure 3 Schematic diagram of unit warping angle.

[0058] Figure 4 Schematic diagram of the Jacobi ratio.

[0059] Figure 5 is the ellipse controlled by the Riemann metric matrix.

[0060] Figure 6 The ideal u and v directions and dimensions provided by the present invention.

[0061] Figure 7 This is the ideal quadrilateral provided by the present invention.

[0062] Figure 8 The area of ​​overlap between the converted figure provided by the present invention and the ideal quadrilateral.

[0063] Figure 9 This is the actual quadrilateral mesh provided in Example 1 of the present invention.

[0064] Figure 10 These are the ideal u and v directions provided by Example 1 of the present invention.

[0065] Figure 11 This is the ideal quadrilateral provided in Example 1 of the present invention.

[0066] Figure 12 The actual quadrilateral after scaling provided by embodiment 1 of the present invention

[0067] Figure 13 The overlapping area between the scaled quadrilateral and the ideal quadrilateral provided in embodiment 1 of the present invention.

[0068] Figure 14 This is a quadrilateral 1 obtained by converting the triangular mesh provided by the present invention.

[0069] Figure 15 This is quadrilateral 2 obtained by converting the triangular mesh provided by the present invention.

[0070] Figure 16 The same quadrilateral is obtained by converting different triangular meshes provided by the present invention.

[0071] Figure 17 This is the triangular mesh provided by Example 2 of the present invention.

[0072] Figure 18 This is a quadrilateral converted from the triangular mesh provided in Example 2 of the present invention.

[0073] Figure 19 The ideal quadrilateral mesh corresponding to the triangular mesh provided in Example 2 of the present invention.

[0074] Figure 20 The overlapping area between the quadrilateral converted from the triangular mesh provided in embodiment 2 of the present invention and the ideal quadrilateral after scaling. DETAILED DESCRIPTION

[0075] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0076] In the generation of unstructured grids, background grid technology is generally used to more precisely control the length scale of each location. This is used to determine the size of each grid. The background grid is generated before the actual grid is generated. The characteristic length required for each location is pre-arranged within the grid area to be generated. For example, in areas with gentle changes, a larger grid is generated, while in areas with drastic changes or sharp shapes, a smaller grid is required. This information is stored in the background grid. Since this information cannot be accurately stored for every point in the area, a series of points are arranged to store this information. The information of the remaining points is obtained from the difference between these points. The method used to generate these points for storing information is the same or similar to the method used to generate the grid points, so this set of points is called the background grid.

[0077] In order to store the characteristic lengths of each direction at each point, it is impossible to list all directions. Therefore, many researchers use the Riemann metric to store the scales of each direction in the background grid. In this way, only the lengths of the major and minor axes of the ellipse and the rotation angle of the ellipse need to be stored to represent an elliptical anisotropic scale.

[0078] For the convenience of storage, the present invention simplifies the background grid data. As long as the rotation angles of a point along the u and v directions and the ideal size value are saved, we can easily obtain the anisotropic size in any direction and the shape of the ideal grid at the location.

[0079] Based on this, this paper proposes a more suitable quality assessment method for anisotropic meshes: the projected area method. This method primarily assesses the quality of quadrilateral and triangular meshes. For generated meshes, we aim to ensure that they closely match the anisotropic properties of the corresponding positions in the background mesh. This means that the ideal lengths of both the u and v direction vectors are met. This results in an optimal anisotropic mesh quality.

[0080] After the grid is generated, the ideal lengths of its u and v direction vectors can be found in its background grid, such as Figure 6 As shown in , a complete parallelogram is formed by making parallel lines, that is, the ideal quadrilateral mesh corresponding to the actual mesh, as shown in Figure 7 shown.

[0081] Then, the quadrilateral mesh or triangular mesh is transformed according to certain rules so that the transformed graphics represent the anisotropic characteristics of the original mesh and coincide with the center of the ideal quadrilateral. The overlapping area of ​​the two graphics is calculated, such as Figure 8 As shown, the similarity between the actual grid and the ideal grid is judged and the grid quality is determined. The larger the ratio of the overlapping area to the area of ​​the rational grid, the higher the grid quality.

[0082] The method of the present invention is described below in detail by taking the quality judgment method of quadrilateral mesh and triangular mesh as an example.

[0083] (1) Quadrilateral mesh quality judgment

[0084] For the generated quadrilateral mesh, the quality of the mesh is reflected in the following two aspects:

[0085] 1. Whether the actual quadrilateral mesh area is close to the ideal quadrilateral mesh area at its location.

[0086] 2. Whether the anisotropic size of the actual quadrilateral in the u and v directions is close to the anisotropic size of the ideal quadrilateral mesh in the u and v directions at its location.

[0087] Therefore, we set two parameters α1 and α2 to characterize the properties of the quadrilateral mesh in the above two aspects respectively. The mesh quality Qquad = α1*α2.

[0088] α1=min(S 实 , S 理 ) / max(S 实 , S 理 )

[0089] Among them S 实 is the area of ​​the actual quadrilateral mesh, S 理 is the area of ​​the ideal quadrilateral mesh. The closer α1 is to 1, the closer the actual mesh area is to the ideal mesh area, and the higher the mesh quality.

[0090] α2=S 重合 / S 理

[0091] To judge the anisotropy of the actual quadrilateral mesh, first scale the mesh up or down proportionally so that its area is equal to that of the ideal quadrilateral mesh, then overlap it with the center of the ideal quadrilateral and project the actual quadrilateral onto the plane of the ideal quadrilateral to calculate the overlap area S. The closer the overlap area is to the area of ​​the ideal mesh, the closer α2 is to 1, and the higher the mesh quality is. So use Q 四边形 =α1*α2 to represent the mesh quality of the quadrilateral, Q 四边形 When =1, the grid is most ideal.

[0092] Example 1

[0093] like Figure 9 As shown, it is an actual quadrilateral mesh with a short side of 40°, a long side of 60°, and an angle of 60°. Then S 实 =2077.

[0094] like Figure 10 As shown, the u, v directions Su, Sv and lengths stored in the background grid at the actual quadrilateral grid position are drawn as parallel lines to form a parallelogram PUQV, which is the ideal quadrilateral grid corresponding to this actual quadrilateral grid, as shown Figure 11 As shown, S 理 =1736,α1=min(S 实 , S 理 ) / max(S 实 , S 理 )=0.8358.

[0095] like Figure 12 As shown in , the actual quadrilateral mesh is scaled proportionally so that its area is equal to the area of ​​the ideal quadrilateral, and then the scaled quadrilateral is aligned with the center of the ideal quadrilateral, as shown in Figure 13 As shown, calculate the overlapping area S 重合 =1256,α2=S 重合 / S 理 =0.7235.

[0096] So the mesh quality of this actual quadrilateral is Q 四边形 =α1*α2=0.6047.

[0097] (2) Triangular mesh quality judgment

[0098] Since the ideal meshes in the background mesh are all stored in quadrilateral format, it is difficult to project the actual triangular mesh onto the ideal quadrilateral. Therefore, it is necessary to first convert the triangular mesh into an anisotropic quadrilateral mesh. For the actual triangular mesh, the u and v directions of its ideal mesh are obtained, and the straight lines in the u and v directions are translated up, down, left, and right respectively, so that the parallelogram composed of the four sides can just surround the triangle. This parallelogram can represent the anisotropic characteristics of the triangle in the u and v directions. Figure 14 and 15 For the same triangle mesh in two different sets of u, v directions l AB 、l AD The two parallelograms are converted into the same shape in the same direction. The quality of the triangle mesh is then calculated based on the overlapping area using the method used to determine the quality of the quadrilateral mesh.

[0099] We set three parameters β1, β2, and β3 to characterize the properties of the triangular mesh, the mesh quality Q 三角形 =β1*β2*β3

[0100] β1=2*S 三角形 / S 平行四边形

[0101] For triangles ADE, BDE, and CDE, if the u and v directions of their ideal grids are l AE 、l FE , translate these two straight lines and make parallel lines between them. Finally, the four sides can just surround the triangle without passing through the triangle, forming a parallelogram AEFD, as shown in Figure 16 As shown in the figure, the three different triangular meshes produce the same parallelogram after conversion, but triangle ADE better matches the anisotropy of the background mesh and has the best quality, while triangle CDE has the worst quality. The best mesh quality occurs when the area of ​​the triangle is half the area of ​​the converted parallelogram, and β1 is 1. As β1 decreases, the mesh quality deteriorates. The parameter β1 is used to represent this property.

[0102] Where Sparallelogram is the area of ​​the converted quadrilateral mesh, Stheoretical is the area of ​​the ideal quadrilateral mesh, and the closer β2 is to 1, the closer the actual mesh area is to the ideal mesh area, and the higher the mesh quality.

[0103] β3=S 重合 / S 理

[0104] The converted quadrilateral mesh is proportionally enlarged or reduced to make its area equal to that of the ideal quadrilateral mesh, and then overlapped with the center of the ideal quadrilateral, and the actual quadrilateral is projected onto the plane of the ideal quadrilateral, and the overlap area S is calculated. The closer the overlap area is to the area of ​​the ideal mesh, the closer β3 is to 1, and the higher the mesh quality is. So use Q 三角形 =β1*β2*β3 to represent the quality of the triangle mesh, Q 三角形 When =1, the grid is most ideal.

[0105] Example 2

[0106] Figure 17 is the actual triangle mesh S 三角形 =451, its u and v directions in the background grid are l AB 、l AD , the transformed parallelogram is ABCD, such as Figure 18 As shown, the area is S 平行四边形 =1777, β1=2*S 三角形 / S 平行四边形 =0.5076.

[0107] Figure 19 The ideal quadrilateral mesh corresponding to the triangular mesh has an area of ​​S 理 =1818,β2=min(S 平行四边形 , S 理 ) / max(S 平行四边形 , S 理 )=0.9774, scale the converted quadrilateral to coincide with the center of the ideal quadrilateral, such as Figure 20 As shown, calculate the overlapping area S 重合 =1532,β3=S 重合 / S 理 =0.8423.

[0108] This method accurately assesses the quality of anisotropic meshes by comparing the actual mesh with an ideal mesh in the background mesh. Mesh quality is converted into the area of ​​overlap between two shapes, resulting in a more intuitive and understandable result with fewer calculation steps and faster computation. This method can provide scientific guidance for mesh optimization, generating higher-quality anisotropic meshes.

[0109] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for judging the quality of anisotropic meshes, characterized in that: The steps include: S1: For a generated quadrilateral mesh or triangular mesh, find the ideal lengths of its u and v direction vectors in the background mesh, and draw parallel lines to form a complete parallelogram, which is the ideal quadrilateral mesh corresponding to the actual mesh. S2: Convert the quadrilateral mesh or triangular mesh separately so that the converted graphics can represent the anisotropic characteristics of the original mesh and coincide with the center of the ideal quadrilateral, and calculate the overlapping area of ​​the two graphics; S3: Determine the mesh quality by judging the similarity between the actual mesh and the ideal mesh based on the overlap area; For the generated quadrilateral mesh, the mesh quality Q 四边形 =α1*α2, α1=min(S 实 , S 理 ) / max(S 实 , S 理 ), α2=S 重合 / S 理 , where S 实 is the area of ​​the actual quadrilateral mesh, S 理 is the area of ​​the ideal quadrilateral mesh, α1 and α2 are two parameters that are set. α1 represents the closeness between the actual mesh area and the ideal mesh area, and α2 represents the closeness between the anisotropic size of the actual quadrilateral in the u and v directions and the anisotropic size of the ideal quadrilateral mesh in the u and v directions at its location. For the generated triangular mesh, the mesh quality Q 三角形 =β1*β2*β3, β1=2*S 三角形 / S 平行四边形 , β2=min(S 平行四边形 , S 理 ) / max(S 平行四边形 , S 理 ), β3=S 重合 / S 理 , where S 平行四边形 is the area of ​​the converted quadrilateral mesh, S 理 is the area of ​​the ideal quadrilateral mesh, β1, β2, and β3 are three parameters that are set. β1 represents the degree of closeness between the actual triangular mesh and the area of ​​the converted parallelogram, β2 represents the degree of closeness between the area of ​​the converted parallelogram and the ideal mesh, and β3 represents the degree of closeness between the anisotropic size of the converted parallelogram in the u and v directions and the anisotropic size of the ideal quadrilateral mesh at its location in the u and v directions.

2. The method for judging the quality of anisotropic mesh according to claim 1, characterized in that: For a quadrilateral mesh, the overlapping area calculation process in step S2 is as follows: first, the quadrilateral mesh is proportionally enlarged or reduced so that its area is equal to the area of ​​the ideal quadrilateral mesh, then it is coincident with the center of the ideal quadrilateral, and the actual quadrilateral is projected onto the ideal quadrilateral plane to calculate the overlapping area S 重合 , the closer the overlapping area is to the area of ​​the ideal grid, the higher the grid quality.

3. The method for judging the quality of anisotropic mesh according to claim 1, characterized in that: In step S2, for the generated triangular mesh, it is first necessary to convert the triangular mesh into an anisotropic quadrilateral mesh.

4. The method for judging the quality of anisotropic mesh according to claim 3, characterized in that: The process of converting a triangular mesh into an anisotropic quadrilateral mesh is as follows: obtain the ideal u and v directions of the triangular mesh, and translate the straight lines in the u and v directions up, down, left, and right respectively, so that the parallelogram composed of the four sides just surrounds the triangle. At this time, the parallelogram represents the anisotropic characteristics of the triangle in the u and v directions.

5. The method for judging the quality of anisotropic mesh according to claim 1, characterized in that: For triangular meshes, the overlapping area calculation process in step S2 is as follows: the converted quadrilateral mesh is proportionally enlarged or reduced to make its area equal to the area of ​​the ideal quadrilateral mesh, and then coincides with the center of the ideal quadrilateral, and the actual quadrilateral is projected onto the ideal quadrilateral plane to calculate the overlapping area S 重合 , the closer the overlapping area is to the area of ​​the ideal grid, the higher the grid quality.

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